A comprehensive comparison of the performance of metaheuristic algorithms in neural network training for nonlinear system identification

Abstract

Many problems in daily life exhibit nonlinear behavior. Therefore, it is important to solve nonlinear problems. These problems are complex and difficult due to their nonlinear nature. It is seen in the literature that different artificial intelligence techniques are used to solve these problems. One of the most important of these techniques is artificial neural networks. Obtaining successful results with an artificial neural network depends on its training process. In other words, it should be trained with a good training algorithm. Especially, metaheuristic algorithms are frequently used in artificial neural network training due to their advantages. In this study, for the first time, the performance of sixteen metaheuristic algorithms in artificial neural network training for the identification of nonlinear systems is analyzed. It is aimed to determine the most effective metaheuristic neural network training algorithms. The metaheuristic algorithms are examined in terms of solution quality and convergence speed. In the applications, six nonlinear systems are used. The mean-squared error (MSE) is utilized as the error metric. The best mean training error values obtained for six nonlinear systems were 3.5×10−4, 4.7×10−4, 5.6×10−5, 4.8×10−4, 5.2×10−4, and 2.4×10−3, respectively. In addition, the best mean test error values found for all systems were successful. When the results were examined, it was observed that biogeography-based optimization, moth–flame optimization, the artificial bee colony algorithm, teaching–learning-based optimization, and the multi-verse optimizer were generally more effective than other metaheuristic algorithms in the identification of nonlinear systems.